1 citations · 1 across the 11 of their papers we have counts for
13 papers
Piggybacking over unbounded distributive lattices
Leonardo M. Cabrer, Hilary A. Priestley
This paper fills a gap in the literature on natural duality theory. It concerns dual representations of categories of distributive-lattice-based algebras in which the lattice reduc…
Sugihara algebras and monoids: multisorted dualities
L. M. Cabrer, H. A. Priestley
The authors developed in a recent paper natural dualities for finitely generated quasivarieties of Sugihara algebras. They thereby identified the admissibility algebras for these q…
Sugihara Algebras: Admissibility Algebras via the Test Spaces Method
Leonardo Cabrer, Hilary Priestley
This paper studies finitely generated quasivarieties of Sugihara algebras. These quasivarieties provide complete algebraic semantics for certain propositional logics associated wit…
Checking Admissibility Using Natural Dualities
Leonardo M. Cabrer, Benjamin Freisberg, George Metcalfe +1
This paper presents a new method for obtaining small algebras to check the admissibility-equivalently, validity in free algebras-of quasi-identities in a finitely generated quasiva…
Natural dualities through product representations: bilattices and beyond
Leonardo Cabrer, Hilary Priestley
This paper focuses on natural dualities for varieties of bilattice-based algebras.Such varieties have been widely studied as semantic models in situations where information is inco…
Bohr compactifications of algebras and structures
B. A. Davey, M. Haviar, H. A. Priestley
This paper provides a unifying framework for a range of categorical constructions characterised by universal mapping properties, within the realm of compactifications of discrete s…
A general framework for product representations: bilattices and beyond
L. M. Cabrer, H. A. Priestley
This paper studies algebras arising as algebraic semantics for logics used to model reasoning with incomplete or inconsistent information. In particular we study, in a uniform way,…
Piggyback dualities revisited
B. A. Davey, M. Haviar, H. A. Priestley
In natural duality theory, the piggybacking technique is a valuable tool for constructing dualities. As originally devised by Davey and Werner, and extended by Davey and Priestley,…
Gödel algebras: interactive dualities and their applications
Leonardo M. Cabrer, Hilary A. Priestley
We present a technique for deriving certain new natural dualities for any variety of algebras generated by a finite Heyting chain. The dualities we construct are tailored to admit…
Product representation for default bilattices: an application of natural duality theory
L. M. Cabrer, A. P. K. Craig, H. A. Priestley
Bilattices (that is, sets with two lattice structures) provide an algebraic tool to model simultaneously the validity of, and knowledge about, sentences in an appropriate language.…
A fresh perspective on canonical extensions for bounded lattices
A. P. K. Craig, M. Haviar, H. A. Priestley
This paper presents a novel treatment of the canonical extension of a bounded lattice, in the spirit of thetheory of natural dualities. At the level of objects, this can be achieve…
Coproducts of distributive lattice-based algebras
L. M. Cabrer, H. A. Priestley
This paper presents a systematic study of coproducts. This is carried out principally, but not exclusively, for finitely generated quasivarieties A that admit a (term) reduct in th…
Distributive bilattices from the perspective of natural duality theory
L. M. Cabrer, H. A. Priestley
This paper provides a fresh perspective on the representation of distributive bilattices and of related varieties. The techniques of naturalduality are employed to give, economical…